# GMAT Math : Understanding arithmetic sets

## Example Questions

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### Example Question #1 : Understanding Arithmetic Sets

Which set is NOT equal to the other sets?

Explanation:

Order and repetition do NOT change a set.  Therefore, the set we want to describe contains the numbers 1, 3, and 4.  The only set that doesn't contain all 3 of these numbers is , so it is the set that does not equal the rest of the sets.

### Example Question #1 : Arithmetic

Given the sets A = {2, 3, 4, 5} and B = {3, 5, 7}, what is ?

Explanation:

We are looking for the union of the sets.  That means we want the elements of A OR B.

So = {2, 3, 4, 5, 7}.

### Example Question #1 : Sets

Given the set  = {2, 3, 4, 5}, what is the value of ?

Explanation:

We need to add 3 to every element in .

Then:

### Example Question #1 : Arithmetic

There exists two sets  and .   = {1, 4} and  = {3, 4, 6}.  What is ?

Explanation:

Add each element of  to each element of .

= {1 + 3, 1 + 4, 1 + 6, 4 + 3, 4 + 4, 4 + 6} = {4, 5, 7, 8, 10}

### Example Question #2 : Arithmetic

How many functions map from  to ?

Explanation:

There are three choices for  (1, 2, and 3), and similarly there are three choices for  (also 1, 2, and 3).  Together there are  possible functions from  to .  Remember to multiply, NOT add.

### Example Question #6 : Understanding Arithmetic Sets

How many elements are in a set from which exactly 768 unique subsets can be formed?

It is not possible to form exactly 768 unique subsets.

It is not possible to form exactly 768 unique subsets.

Explanation:

The number of subsets that can be formed from a set with  elements is . However,  and , so there is no integer  for which . Therefore, a set with exactly 768 elements cannot exist.

### Example Question #3 : Arithmetic

Let the univeraal set  be the set of all positive integers.

Define the sets

,

,

.

If the elements in  were ordered in ascending order, what would be the fourth element?

Explanation:

are the sets of all positive integers that are one greater than a multiple of five, four, and three, respectively. Therefore, for a number to be in all three sets, and subsequently, , the number has to be one greater than a number that is a multiple of five, four, and three. Since , the number has to be one greater than a multiple of 60. The first four numbers that fit this description are 1, 61, 121, and 181, the last of which is the correct choice.

### Example Question #1 : Sets

A six-sided die is rolled, and a coin is flipped. If the coin comes up heads, the roll is considered to be the number that appears face up on the die; if the coin comes up tails, the outcome is considered to be twice that number. What is the sample space of the experiment?

Explanation:

If heads comes up on the coin, the number on the die is recorded. This can be any element of the set .

If tails comes up on the coin, twice the number on the die is recorded. This can be twice any element of the set  - that is, any element of the set .

The sample space is the union of these two sets:

### Example Question #4 : Arithmetic

A six-sided die is rolled, and a coin is flipped. If the coin comes up heads, the roll is considered to be the number that appears face up on the die; if the coin comes up tails, the outcome is considered to be half that number, with any fraction simply thrown out. What is the sample space of the experiment?

Explanation:

If heads comes up on the coin, the number on the die is recorded. This can be any element of the set .

If tails comes up on the coin, half the number on the die is recorded, and any fraction is thrown out. Half the elements of the set  comprise the set  , but since we are throwing out the fractional parts, this becomes the set

The sample space is the union of these two sets, which is .

### Example Question #1 : Arithmetic

Refer to the above graph, which shows the peak temperature in Smithville for each of seven days in a one-week period.

Between which two consecutuve days did the peak temperature see its greatest decrease?

Friday to Saturday

Tuesday to Wednesday

Wednesday to Thursday

Thursday to Friday

Monday to Tuesday